Page 81 - 04. Subyek Engineering Materials - Manufacturing, Engineering and Technology SI 6th Edition - Serope Kalpakjian, Stephen Schmid (2009)

60 Chapter 2 Mechanical Behavior, Testing, and Manufacturing Properties of Materials

60 value of the ratio of the lateral strain to the lon-
gitudinal strain is known as Poisson’s ratio (after
A 50 _ S.D. Poisson, 1781-1840) and is denoted by the
Q Stainless steels,
L annealed Symbol V'
E E 4o-
g 2.2.2 Ductility
30 - Copperand IIS Alumlnum An important behavior observed during a ten-
.
ug 20 _ alloys, annealed alloys’ annealed sion test is ductility-the extent of plastic defor-
Elongation =f
§° Lowcarbon Stee|SI mation that the material undergoes before
E Com roued fracture. There are two common measures of
10 _ . . .
ductility. The first is the total elongation of the
O specimen, given by
0 10 20 30 40 50 60 70 80 90 (lf _ lo)
Reduction of area (%) >< 100, (2.4)
O
FIGURE 2.4 Approximate relationship between elongation and Where If and lo are measured 35 Shown in
tensile reduction of area for various groups of metals. Fig- 2-13. Note that £116 €lO11gatiOHis based OH
the original gage length of the specimen and that
it is calculated as a percentage.
Reduction of area =~ >< 100, (2.5)
The second measure of ductility is the reduction of area, given by
(AO * Af)

where AO and Af are, respectively, the original and final (fracture) cross-sectional
areas of the test specimen. Reduction of area and elongation are generally interrelat-
ed, as shown in Fig. 2.4 for some typical metals. Thus, the ductility of a piece of
chalk is zero, because it does not stretch at all or reduce in cross section; by contrast,
a ductile specimen, such as putty or chewing gum, stretches and necks considerably
before it fails.

2.2.3 True Stress and True Strain

Engineering stress is based on the original cross-sectional area, AO, of the specimen.
However, the instantaneous cross-sectional area of the specimen becomes smaller as
it elongates, just as the area of a rubber band does; thus, engineering stress does not
represent the actual stress to which the specimen is subjected.
True stress is defined as the ratio of the load, R to the actual (instantaneous,
hence true) cross-sectional area, A, of the specimen:
P
0 = Z. (2.6)

For true strain, first consider the elongation of the specimen as consisting of
increments of instantaneous change in length. Then, using calculus, it can be shown
that the true strain (natural or logarithmic strain) is calculated as
6 = ln (2.7)

Note from Eqs. (2.2) and (2.7) that, for small values of strain, the engineering
and true strains are approximately equal. However, they diverge rapidly as the strain
increases. For example, when e = 0.1, e = 0.095 and when e = 1, e = 0.69.
,
Unlike engineering strains, true strains are consistent with actual physical phe-
nomena in the deformation of materials. Let’s assume, for example, a hypothetical
~